06. Pilar Pte Quilca

Proyecto: Estudio Definitivo de la carretera: Camana - Desvio Quilca - Matarani - Ilo - Tacna, Tramo: Desvio Quilca - Matrani

Descripción del Trabajo: Diseño Pilar Pte Quilca

1.00 GEOMETRÍADATOS

b1 h = 7.60 m altura total

b2 b1 = 8.90 m

b2 = 6.50 m

h1 b3 = m

d4 = 0.00 m

h2 d5 = 0.00 m

d6 = 12.00 m

h1 = 1.00 m

h2 = 0.50 m

h3 = 4.50 m

h3 h4 = 0.00 m

h5 = 0.00 m

h6 = 1.60 m

ht = 1.76 m

ht h4 t1 = 1.40 m

d4 t2 = 1.20 m

h5 t3 = m

d5 t4 = m

h6 t5 = 12.00 m

DESARROLLO REFERENCIA

"PILAR " - PUENTE QUILCA

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h6 t5 = 12.00 m

d6 # Columnas = 1

e = 0.00 m

p adm. = 0.00 ton/m2

f¨ce = 210.00 Kg/cm2

e f´cz = 210.00 k/cm3

pet = 1.80 ton/m3 peso especifico suelo

pec elev. = 2.40 ton/m3

t1 h1 pec zap. = 2.40 ton/m3

h2 puadm = 0.00 ton/m2

V viento = 100.00 km/hora

p vient. S/c = 150.00 k/m

h3 Luz = 30.00 m

t2 altura viga = 2.50 m

t3 P DC 1 = 666.76 ton

P DW 1 = 131.52 ton

h4 P LL+IM1 = 216.60 ton

t4 altura total = 7.60 m

h5 altura elev. = 6.00 m

Cx = 1.00 Coef. Sismico Dirección X

h6 Cy = 1.00 Coef. Sismico Dirección Y

u = 0.287 fricción

t5 c = 0.000 Kg/cm2

altura cim. = 1.60 m


Descripción del Trabajo: Diseño Pilar Pte QuilcaDESARROLLO REFERENCIA

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8.90 e

6.50

1.00 1.40 1.00

0.50 0.50

4.50 4.50

1.20

ht

1.60 1.60

12.00 12.00

Y

12.00

12.00

X --> Tránsito

PLANTA

TABLE: Element Forces - FramesFrame Station OutputCase StepType P V2 V3 M2 M3

Text m Text Text Tonf Tonf Tonf Tonf-m Tonf-m

4 6 SX Max 13.325 224.510 184.765 1108.591 1347.058

1328 6 SX Max 6.435 216.392 203.188 1219.126 1298.354

1649 6 SX Max 3.175 193.536 85.804 514.823 1161.217

1970 6 SX Max 13.031 162.403 197.574 1185.446 974.421

2291 6 SX Max 27.064 122.766 202.178 1213.069 736.596



4 6 SY Max 3.998 67.353 615.884 3695.302 404.117

1328 6 SY Max 1.931 64.918 677.292 4063.754 389.506

1649 6 SY Max 0.952 58.061 286.013 1716.078 348.365



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4 6 SX Max 19.050 166.832 194.820 1168.921 1000.991

1328 6 SX Max 15.667 161.171 216.067 1296.404 967.023

1649 6 SX Max 9.628 145.682 105.056 630.336 874.091

1970 6 SX Max 37.637 142.525 217.073 1302.439 855.147

2291 6 SX Max 45.901 174.020 174.930 1049.577 1044.1192291 6 SX Max 45.901 174.020 174.930 1049.577 1044.119



4 6 SY Max 5.715 50.050 649.401 3896.405 300.297

1328 6 SY Max 4.700 48.351 720.224 4321.346 290.107

1649 6 SY Max 2.889 43.705 350.187 2101.119 262.227

1970 6 SY Max 11.291 42.757 723.577 4341.464 256.544

2291 6 SY Max 13.770 52.206 583.099 3498.591 313.236

2.00 FUERZAS APLICADAS

2.10 Peso propio (P DC )

En sentido del tránsito

En sentido del tránsito

Cabezal 1.40 8.90 1.00 2.40 29.904 29.904 212.318

Cabezal 1.30 7.70 0.50 2.40 12.012 12.012 77.277

Columna Area

14.245 4.50 2.40 153.846 153.846 592.307

Zapata 1 0.00 0.00 0.00 2.40 0.000 0.000 0.000

Zapata 2 0.00 0.00 0.00 2.40 0.000 0.000 0.000

Zapata 3 12.00 12.00 1.60 2.40 552.960 552.960 442.368

Q = Σ = 748.722 748.722 1324.271

Relleno 1 1.80 0.000

Relleno 2 12.00 12.00 0.16 1.80 41.472

Q = Σ = 41.472

MEQyBLOQUElargo

(m)

ancho

(m)

alto

(m)

pe

(ton/m3)Fv (ton) EQx



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Transversal al tránsito

Cabezal 8.90 1.40 1.00 2.40 29.904 29.904 212.318

Cabezal 7.70 1.30 0.50 2.40 12.012 12.012 77.277

Columna Area

14.245 4.50 2.40 153.846 153.846 592.307

Zapata 1 0.00 0.00 0.00 2.40 0.000 0.000 0.000

Zapata 2 0.00 0.00 0.00 2.40 0.000 0.000 0.000

Zapata 3 12.00 12.00 1.60 2.40 552.960 552.960 442.368

Q = Σ = 748.722 748.722 1324.271

Relleno 1 1.80 0.000

Relleno 2 12.00 12.00 0.16 1.80 41.472

Q = Σ = 41.472

2.20 Reacciones del puente (D,L)

R DC = 666.760 ton → Mry. DC = 4000.560 ton-m

Mrx. DC = 4000.560 ton-m

R DW = 131.520 ton → Mry. DW = 789.120 ton-m

Mrx. DW = 789.120 ton-m

R LL+IM = 216.600 ton → Mry. LL+IM = 1299.600 ton-m

Mrx. LL+IM = 1299.600 ton-m

2.30 Sismo ( EQ ) debido R DC

EQx = 666.76 ton M EQy = 5067.376 ton-m

BLOQUElargo

(m)

ancho

(m)

alto

(m)

pe

(ton/m3)Fv (ton) EQy MEQx

EQy = 666.76 ton M EQx = 5067.376 ton-m

2.40 Frenado ( BR )

peso truck → 33.16 8.29 ton truck+wl 61.66 3.08 ton

peso tandem → 22.44 5.61 ton tandem+wl 50.94 2.55 ton

BR= 8.29 ton Mvx= 0 ton-m

Mvy= 77.926 ton-m

2.70 Fuerza del viento ( WS, WL)

Velocidad del viento 100 km/hora h = 7600 mm

Vo = 13.2 Zo = 70 Pb = 0.0024

Vdz = 96.68 km/hora P = 0.001 Mpa → 0.008762 ton/m2

WSx = 0.063 ton Mws.y = 0.268 ton-m

WSy = 0.720 ton Mws.x = 3.061 ton-m

2.90 PilotesDimensiones de Pilote: D m) = 1.20

A (m2) = 1.13

f'c = 280 Kg/cm2

Vc. Pilote = 84.28 ton/pilote

Capacidad de pilote = 150.0 ton

→ # Pilotes = 13 → Se usaran = 16 pilotes

Servicio

Maximo Minimo Maximo Minimo Maximo Minimo Maximo Minimo

P DC 1.25 0.90 1.25 0.90 1.00 1.25 0.90 1.25 0.90

R DC 1.25 0.90 1.25 0.90 1.00 1.25 0.90 1.25 0.90

R DW 1.50 0.65 1.50 0.65 1.00 1.50 0.65 1.50 0.65

R LL+IM 1.75 1.75 1.35 0.00 1.00 0.50 0.00 0.50 0.00

EV 1.35 1.00 1.00 1.35 1.00 1.35 1.00

BR 1.75 1.75 1.00 0.50 0.00 0.50 0.00

WS 1.40 1.40 1.00

EQx 1.00 1.00 0.30 0.30

EQy 0.30 0.30 1.00 1.00

FACTORES DE CARGA

CargaResistencia I Resistencia III Extremo X Extremo Y



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Carga P (ton) Vx (ton) My (ton-m) P (ton) Vy (ton) Mx (ton-m) Resistencia Extremo

P DC 748.72 748.72 Volteo 0.90 1.00

R DC 666.76 666.76 Deslizam 0.80 1.00

R DW 131.52 0.20 131.52 Presion 0.45 1.00

R LL+IM 216.60 4.72 216.60 21.49

EV 41.47 41.47

BR 13.20 77.93

WS 0.06 0.27 0.72 3.06

EQ 13.32 224.51 1347.06 11.29 723.58 4341.46

3.00 ESTABILIDAD Y PRESIONES

3.10 Sentido del TránsitoBx = 12.00 m

By = 12.00 m

Excentricidad

Resistencia I 2401.67 136.37 0.00 0.057 0.000 3.000 98.1Resistencia I-a 1779.94 136.37 0.00 0.077 0.000 3.000 97.4Resistencia III 2259.04 0.38 0.00 0.000 0.000 3.000 100.0Resistencia III-a 1359.42 0.38 0.00 0.000 0.000 3.000 100.0Servicio I 1805.07 78.19 0.00 0.043 0.000 3.000 98.6Evento Ext. I 2144.24 11063.57 1302.44 5.160 0.607 4.400 -17.3

Margen de

Diseño (%)Fv My Mx ex ey e.máx

CARGAS (Paralelo al Tránsito) CARGAS (Transversal al Tránsito) FACTORES DE RESISTENCIA

Evento Ext. I 2144.24 11063.57 1302.44 5.160 0.607 4.400 -17.3Evento Ext. I-a 1414.22 6809.47 1302.44 4.815 0.921 4.000 -20.4

Deslizamiento

Resistencia I 2401.67 1348.50 0.800 1078.80 31.65 97.1Resistencia I-a 1779.94 1348.50 0.800 1078.80 31.48 97.1Resistencia III 2259.04 1348.50 0.800 1078.80 6.76 99.4Resistencia III-a 1359.42 1348.50 0.800 1078.80 0.22 100.0Servicio I 1805.07 1348.50 0.800 1078.80 18.18 98.3Evento Ext. I 2144.24 1348.50 1.000 1348.50 118.21 91.2Evento Ext. I-a 1414.22 1348.50 1.000 1348.50 124.77 90.7

Capacidad de Carga en Pilote

Servicio I 1805.07 1.00 12.63 113.64 150.00 24.2

3.20 Transversal al TránsitoBy = 12.00 m

Bx = 12.00 m

Excentricidad

Resistencia I 2401.67 0.00 0.00 0.000 0.000 3.000 100.0Resistencia I-a 1779.94 0.00 0.00 0.000 0.000 3.000 100.0Resistencia III 2259.04 4.29 0.00 0.002 0.000 3.000 99.9Resistencia III-a 1359.42 4.29 0.00 0.003 0.000 3.000 99.9Servicio I 1805.07 3.06 0.00 0.002 0.000 3.000 99.9Evento Ext. I 2142.21 8108.13 404.12 3.785 0.189 4.400 14.0Evento Ext. I-a 1412.18 3815.07 404.12 2.702 0.286 4.000 32.5

φFvqmax

(ton/m2)

Fp

(ton)

Capacidad

Pilote

(ton)

Margen de

Diseño (%)

Margen de

Diseño (%)Fv Mx My ey ex e.máx

Fv #Vc φ φ.(#Vc) FhMargen de

Diseño (%)



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Deslizamiento

Resistencia I 2401.67 1348.50 0.800 1078.80 37.60 96.5Resistencia I-a 1779.94 1348.50 0.800 1078.80 37.60 96.5Resistencia III 2259.04 1348.50 0.800 1078.80 30.01 97.2Resistencia III-a 1359.42 1348.50 0.800 1078.80 1.01 99.9Servicio I 1805.07 1348.50 0.800 1078.80 22.21 97.9Evento Ext. I 2142.21 1348.50 1.000 1348.50 734.32 45.5Evento Ext. I-a 1412.18 1348.50 1.000 1348.50 723.58 46.3

Capacidad de Carga en Pilote

Servicio I 1805.07 1.00 12.54 112.85 150.00 24.8

4.00 DISEÑO DE ELEVACIÓN

P Vx Vy Mx My(Ton) (Ton) (Ton) (Ton-m) (Ton-m)

DC 862.52 0.00 0.00 0.00 0.00

DW 131.52 0.20 0.00 0.00 0.00

R LL+IM 216.60 4.72 0.00 0.00 0.00

EV 41.47 0.00 21.49 0.00 0.00

FvCapacidad

Pilote

(ton)φ

Fp

(ton)

qmax

(ton/m2)

Margen de

Diseño (%)

Fv #Vc φ φ.(#Vc) FhMargen de

Diseño (%)

EV 41.47 0.00 21.49 0.00 0.00

BR 0.00 13.20 0.00 0.00 77.93

WS 0.00 0.06 0.00 3.06 0.27

EQX 13.32 224.51 184.77 1108.59 1347.06

EQY 11.29 42.76 723.58 4341.46 256.54

4.10 VERFICACIÓN POR ESBELTEZ

6.50

1.20

Datos Columna

f'c = 210.00 Kg/cm2

fy = 4200.00 Kg/cm2

Ec = 2.17E+05 Kg/cm2

Hcol = 4.50 m

k = 1.00

A = 7.491 m2

Ix = 24.458 m4

Iy = 0.865 m4

rx = 1.81 m k .l / rx = 2.49 --> Efectos de Esbeltez Despreciablesry = 0.34 m k .l / ry = 13.24 --> Efectos de Esbeltez Despreciables

Calculos Columna:

β dx = 0.00 β dy = 0.00

EIx = 2.13E+07 EIy = 7.52E+05

Pcx = 10364738 Pcy = 366566

Cm = 1.00 Cm = 1.00

Σ Pu = 1710 Σ Pu = 1710

φ = 0.75 φ = 0.75

δ sx = 1.00 δ sy = 1.01



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P Vx Vy Mx My Rx = 2.00

(Ton) (Ton) (Ton) (Ton-m) (Ton-m) Ry = 1.50

DC 862.52 0.00 0.00 0.00 0.00

DW 862.52 0.20 0.00 0.00 0.00

R LL+IM 131.52 4.72 0.00 0.00 0.00

EV 216.60 0.00 21.49 0.00 0.00

BR 41.47 13.20 0.00 0.00 78.41

WS 0.00 0.06 0.00 3.06 0.27

EQX 0.00 112.25 92.38 554.42 677.75

EQY 8.88 28.50 482.38 2894.95 172.10

4.20 COMBINACIONES DE CARGA

P Mx My P Mx My(Ton) (Ton-m) (Ton-m) (KN) (KN-m) (KN-m)

Resistencia I 2967.08 0.00 137.22 29107.07 0.00 1346.17

Resistencia I-a 1856.25 0.00 137.22 18209.76 0.00 1346.17

Resistencia III 2549.49 4.29 0.38 25010.47 42.05 3.71

Resistencia III-a 1336.91 4.29 0.38 13115.08 42.05 3.71

Servicio 2114.64 3.06 78.68 20744.58 30.04 771.89

Evento Extremo X 2750.84 554.42 716.95 26985.76 5438.83 7033.30

Evento Extremo X-a 1553.51 554.42 677.75 15239.92 5438.83 6648.68

Evento Extremo Y 2759.72 2894.95 211.31 27072.90 28399.42 2072.92

Evento Extremo Y-a 1562.39 2894.95 172.10 15327.07 28399.42 1688.30

ESTADOLÍMITE



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→→→→ Usar 152 φφφφ 1"

4.30 CORTANTE

f'c = 210 Kg/cm2

fy = 4200 Kg/cm2

Vx Vy Vu: Cortante máximo en kg

(Ton) (Ton) Vc: Resistencia la corte del concreto en kg

121.51 92.38 Av: Area de acero correspondiente a 1/2"

28.50 511.39

650.00 110.00 121513 549151 59598 547874 2.58 200

120.00 640.00 511390 589857 9082 539045 2.58 200

Vc(kg)

Vs(kg)

Vux(kg)

Av(cm2)

S(mm)

OK!!!

OK!!!

Vu< φφφφ (Vc+Vs)b

(cm)d

(cm)Vuy(kg)

Vc(kg)

Vs(kg)

φφφφ (Vc+Vs)

Vu< φφφφ (Vc+Vs)Av

(cm2)S

(mm)

EVENTO EXTREMO I - x

EVENTO EXTREMO I - y

b(cm)

d(cm)

φφφφ (Vc+Vs)



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5.00 DISEÑO DE ZAPATA

5.21 Sentido del tránsito

♦ Mu(+) = 275.12 ton-m/m fć= 210 Kg/cm2♦ Mu(+) = 275.12 ton-m/m fć= 210 Kg/cm2

b= 100.00 cm fy = 4200 Kg/cm2

d= 122.50 cm →→→→ As= 63.26 cm2

Mínimo Refuerzo

�� Calculo de Mr

→ fr = 28.98 kg/cm2

Mr = 123.66 ton-m

1.2 Mr = 148.39 ton-m

→ As (1.2Mr) = 33.24 cm2

4/3 As = 84.34 cm2 ∴∴∴∴ As.min = 33.24 cm2

Acero de Diseño = 63.26 cm2var. 3/4"@ 25 mm

Usar = var. 1"@ 75 mm

var. 1 3/8"@ 150 mm

♦ Mu(-) = 241.29 ton-m/m fć= 210 Kg/cm2

b= 100.00 cm fy = 4200 Kg/cm2

d= 122.50 cm →→→→ As= 55.01 cm2

Mínimo Refuerzo


→ fr = 28.98 kg/cm2

Mr = 123.66 ton-m

1.2 Mr = 148.39 ton-m

→ As (1.2Mr) = 33.24 cm2

4/3 As = 73.35 cm2 ∴∴∴∴ As.min = 33.24 cm2



var. 1 3/8"@ 175 mm

=2

r

bhM fr

6=

rf 2 f ' c

4, (1.2 )

3mín

As mín As As Mr

=

=2

r

bhM fr

6=

rf 2 f ' c

4, (1.2 )

3mín

As mín As As Mr

=



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5.20 Transversal al tránsito

♦ Mu(+) = 198.49 ton-m/m f´c= 210 Kg/cm2

b= 100.00 cm fy = 4200 Kg/cm2

d= 122.50 cm →→→→ As= 44.79 cm2

Mínimo Refuerzo


→ fr = 28.98 kg/cm2

Mr = 123.66 ton-m

1.2 Mr = 148.39 ton-m

→ As (1.2Mr) = 33.24 cm2

4/3 As = 59.72 cm2 ∴∴∴∴ As.min = 33.24 cm2



var. 1 3/8"@ 200 mm

♦ Mu(-) = 121.23 ton-m/m f´c= 210 Kg/cm2

b= 100.00 cm fy = 4200 Kg/cm2

d= 122.50 cm →→→→ As= 26.87 cm2

Mínimo Refuerzo


→ fr = 28.98 kg/cm2

Mr = 123.66 ton-m

1.2 Mr = 148.39 ton-m

→ As (1.2Mr) = 33.24 cm2

4/3 As = 35.83 cm2 ∴∴∴∴ As.min = 33.24 cm2



var. 1 3/8"@ 300 mm

4, (1.2 )

3mín

As mín As As Mr

=

=2

r

bhM fr

6=

rf 2 f ' c

4, (1.2 )

3mín

As mín As As Mr

=

=2

r

bhM fr

6=

rf 2 f ' c



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6.00 DISEÑO CABEZALf'c = 210 kg/cm2

0.50 fy = 4200 kg/cm2

V DC 1 = 4.03 ton → M DC 1 = 2.42 ton-m

V DC 2 = 0.42 ton → M DC 2 = 0.17 ton-m

1.00 V R DC = 166.69 ton → M R DC = 83.35 ton-m

V R DW = 32.88 ton → M R DW = 16.44 ton-m

V R LL+IM = 54.15 ton → M R LL+IM = 27.08 ton-m

0.50

Vu = 358.01 ton → Mu = 179.46 ton-m

1.20

Nu = 0.2Vu= 71.602 ton

�� TRACCIÓN

b

(cm)

d

(cm)

Pu

(kg)

Fy

(kg/cm2)

A

(cm2)

φ (")

# barrasUsar

# barras

140.00 144.00 71602 4200.00 18.94 3/4 7 7

�� FLEXÍON

b

(cm)

d

(cm)

Mu

(kgxcm)

Ku

(kg/cm2)ρρρρ

A

(cm2)

a

(cm)140.00 144.00 17945650 6.18 0.0017 33.63 5.65

R

Mínimo Refuerzo

Calculo de Mr

→ fr = 28.98 kg/cm2

Mr = 140.23 ton-m

1.2 Mr = 168.28 ton-m

b

(cm)

d

(cm)

Mu

(kgxcm)

Ku

(kg/cm2)ρρρρ

A

(cm2)

a

(cm)140.00 144.00 16827618.5 5.80 0.0016 31.50 5.29

→ As (1.2Mr) = 31.50 cm2

4/3 As = 44.841269 cm2 ∴ As.min = 31.50 cm2

Acero de Diseño = 33.63 cm2 → → → → 12 φ3/4φ3/4φ3/4φ3/4 "

→→→→ Usar : 19 φ3/4φ3/4φ3/4φ3/4 "�� CORTE

140.00 144.00 358010 154837 312077 373531 OK!!! 2.58 100

b(cm)

d(cm)

Vu(kg)

Vc(kg)

Vs(kg)

φφφφ (Vc+Vs) Vu< φφφφ (Vc+Vs)Av

(cm2)s

(mm)

4, (1.2 )

3mín

As mín As As Mr

=

=2

r

bhM fr

6=

rf 2 f ' c

06. Pilar Pte Quilca

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